As a method for compressing sound or image information, there is known a lossless coding method that involves no distortion.
Highly compressive lossless data compression can be achieved by combining a highly compressive lossy coding and a lossless compression of the difference between a reproduced signal of the lossy coding and the original signal. Such a combined compression method has been proposed in the patent literature 1. The method, which is described in detail in the patent literature, will be described briefly below.
In a coder, a frame forming part successively separates digital input signals (referred to also as an input signal sample sequence) into frames, each of which is composed of 1024 input signal samples, for example, and the digital signals are lossily compression-coded on the frame basis. This coding can be based on any format that is suitable for the input digital signal and can reproduce the original digital input signal with a certain fidelity by decoding.
For example, if the digital input signal is a sound signal, a speech coding recommended according to ITU-recommendation G.729 can be used. If the digital input signal is a music signal, a transform-domain weighted interleaved vector quantization (Twin VQ) coding used in MPEG-4 can be used. The code resulting from the lossy compression coding is locally decoded, and a difference signal that represents the difference between the locally decoded signal and the original digital signal is produced. Actually, however, there is no need of local decoding and, instead, it would suffice to obtain the difference between the original digital signal and a quantized signal resulting during the lossy compression coding. The amplitude of the difference signal is typically much smaller than that of the original digital signal. Thus, the quantity of information can be reduced by the lossless compression coding of the difference signal, compared with the lossless compression coding of the original digital signal.
To enhance the efficiency of the lossless compression coding, for a sequence of all the samples of the difference signal in a frame each expressed by sign and magnitude notation (a binary number of sign and magnitude), bits of each position, that is, bits of each of the MSB, the second MSB, . . . , and the LSB are linked along the sample sequence (that is, the time series) to form a respective bit sequence. In other words, the bit arrangement is transformed. For convenience, the bit sequence composed of linked 1024 bits at the equal bit position is referred to as a “coordinate bit sequence”. On the other hand, a one-word bit sequence representing the amplitude value of each sample including its sign is referred to as an “amplitude bit sequence”, for convenience. The difference signal has a small amplitude, and therefore, the most significant bit is, or the most significant bit and the following plural bits are, often all “0”. Thus, by representing the coordinate bit sequence formed by linking the bits at such a bit position, the efficiency of the lossless compression coding of the difference signal can be enhanced.
The coordinate bit sequence is losslessly compression-coded. As the lossless compression coding, an entropy coding, such as Huffman coding and arithmetic coding, can be used which takes advantage of the occurrence or frequent occurrence of a sequence in which the same sign (1 or 0) successively appears.
When decoding, the code resulting from the lossless compression coding is decoded, and the inverse transformation of bit arrangement is performed on the decoded signal. That is, the coordinate bit sequences are transformed into the amplitude bit sequences for each frame, and the resulting difference signals are reproduced sequentially. In addition, the code resulting from the lossy compression coding is decoded, the decoded signal and the reproduced difference signal are summed together, and then, the sum signals for each frame are linked together sequentially, thereby reproducing the original digital signal sequence.
Besides, there are known a variety of lossless coding methods for audio or visual information that permit no distortion. For example, a lossless coding method for music information is disclosed in the non-patent literature 1. Any conventional methods are such one that performs compression coding on a PCM signal directly derived from a signal waveform.
However, in music recording studios, a waveform is sometimes recorded and stored in the floating-point format. Any value in the floating-point format is separated into a sign, an exponent and a mantissa. For example, in the IEEE-754 standard floating-point format shown in FIG. 37, any value consists of 32 bits including 1 bit for sign, 8 bits for exponent and 23 bits for mantissa in the descending order of significance. Denoting the sign by S, the value represented by the 8 bits for exponent by a decimal number E and the binary number for mantissa by M, the value in the floating-point format can be represented in the sign and magnitude binary notation as follows.(−1)S×1.M×2E−E0  (1)
According to the IEEE-754 standard, E0 is defined as E0=27−1=127, so that the “E−E0” in the expression (1) can be any value falling within the range:−127≦E−E0≦128.Here, it is defined that all the bits are set at “0” when E−E0=−127, and all the bits are set at “1” when E−E0=128. The term “E−E0=n” represents a value obtained by subtracting 1 from the number of digits (number of bits) of the integer part of the value represented by the formula (1), that is, the number of bits following the most significant “1”.
In the case where sound, music or image information is represented by a digital signal sequence in the floating-point format, the bit sequence composed of “0”s and “1”s is likely to be random because of the characteristics of the floating-point format. Thus, even if the bit arrangement transformation described above is performed, the entropy compression coding or the like cannot be expected to provide a high compression ratio. Furthermore, the sample sequence in the floating-point format significantly differs from the original analog waveform, so that there is no redundancy resulting from correlation between samples. Therefore, even if the lossless predictive coding method disclosed in the non-patent literature 1 described above is applied, a higher compression ratio cannot be expected.
Patent literature 1: JP Application Kokai Publication No. 2001-44847
Non-patent literature 1: “Lossless Compression of Digital Audio” by Mat Hans, Ronald W. Schafer et al., IEEE SIGNAL PROCESSING MAGAZINE, JULY 2001, pp. 21–32